Category:Radius of Convergence
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This category contains results about Radius of Convergence.
Let $\xi \in \C$ be a complex number.
For $z \in \C$, let:
- $\ds \map f z = \sum_{n \mathop = 0}^\infty a_n \paren {z - \xi}^n$
be a power series about $\xi$.
The radius of convergence is the extended real number $R \in \overline \R$ defined by:
- $R = \ds \inf \set {\cmod {z - \xi}: z \in \C, \sum_{n \mathop = 0}^\infty a_n \paren {z - \xi}^n \text{ is divergent} }$
where a divergent series is a series that is not convergent.
As usual, $\inf \O = +\infty$.
Subcategories
This category has the following 4 subcategories, out of 4 total.
Pages in category "Radius of Convergence"
The following 8 pages are in this category, out of 8 total.